svd_lowrank

paddle.linalg. svd_lowrank ( x, q=None, niter=2, M=None, name=None ) [source]

Return the singular value decomposition (SVD) on a low-rank matrix or batches of such matrices.

If \(X\) is the input matrix or a batch of input matrices, the output should satisfies:

\[X \approx U * diag(S) * V^{T}\]

When \(M\) is given, the output should satisfies:

\[X - M \approx U * diag(S) * V^{T}\]
Parameters

  • x (Tensor) – The input tensor. Its shape should be […, N, M], where … is zero or more batch dimensions. N and M can be arbitrary positive number. The data type of x should be float32 or float64.

  • q (int, optional) – A slightly overestimated rank of \(X\). Default value is None, which means the overestimated rank is 6.

  • niter (int, optional) – The number of iterations to perform. Default: 2.

  • M (Tensor, optional) – The input tensor’s mean. Its shape should be […, 1, M]. Default value is None.

  • name (str, optional) – Name for the operation. For more information, please refer to Name. Default: None.

Returns

  • Tensor U, is N x q matrix.

  • Tensor S, is a vector with length q.

  • Tensor V, is M x q matrix.

tuple (U, S, V): which is the nearly optimal approximation of a singular value decomposition of the matrix \(X\) or \(X - M\).

Examples

>>> import paddle
>>> paddle.seed(2024)

>>> x = paddle.randn((5, 5), dtype='float64')
>>> U, S, V = paddle.linalg.svd_lowrank(x)
>>> print(U)
Tensor(shape=[5, 5], dtype=float64, place=Place(cpu), stop_gradient=True,
[[-0.03586982, -0.17211503,  0.31536566, -0.38225676, -0.85059629],
 [-0.38386839,  0.67754925,  0.23222694,  0.51777188, -0.26749766],
 [-0.85977150, -0.28442378, -0.41412094, -0.08955629, -0.01948348],
 [ 0.18611503,  0.56047358, -0.67717019, -0.39286761, -0.19577062],
 [ 0.27841082, -0.34099254, -0.46535957,  0.65071250, -0.40770727]])

>>> print(S)
Tensor(shape=[5], dtype=float64, place=Place(cpu), stop_gradient=True,
[4.11253399, 3.03227120, 2.45499752, 1.25602436, 0.45825337])

>>> print(V)
Tensor(shape=[5, 5], dtype=float64, place=Place(cpu), stop_gradient=True,
[[ 0.46401347,  0.50977695, -0.08742316, -0.11140428, -0.71046833],
 [-0.48927226, -0.35047624,  0.07918771,  0.45431083, -0.65200463],
 [-0.20494730,  0.67097011, -0.05427719,  0.66510472,  0.24997083],
 [-0.69645001,  0.40237917,  0.09360970, -0.58032322, -0.08666357],
 [ 0.13512270,  0.07199989,  0.98710572,  0.04529277,  0.01134594]])